## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 79

Page 1163

Chang [ 1 ] and [ 2 ]

finite number of operators of Hilbert - Schmidt type . Nikovič [ 1 ] ... Exercises 25

through 36

Chang [ 1 ] and [ 2 ]

**gives**related results dealing with the product of an arbitraryfinite number of operators of Hilbert - Schmidt type . Nikovič [ 1 ] ... Exercises 25

through 36

**give**most known inequalities for the eigenvalues of a finite matrix .Page 1576

( c )

( c )

**give**a complete spectral analysis of the operator in the interval [ 0 , 0 ) , ( d )**give**a complete spectral analysis of the operator in the interval ( - 00 , 0 ] , ( e )**give**a complete spectral analysis of the operator in the interval ( - 00 , + 00 ) .Page 1694

Q . E . D . Sobolev ' s theorems enable us to complete our discussion of the

theory of distributions in several important respects . The next two lemmas

us useful information on the structure of the set D ( I ) of distributions . 13 LEMMA

.

Q . E . D . Sobolev ' s theorems enable us to complete our discussion of the

theory of distributions in several important respects . The next two lemmas

**give**us useful information on the structure of the set D ( I ) of distributions . 13 LEMMA

.

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero